Preheat the oven to 350°F. Grease a 6-inch round cake pan and line the bottom with parchment.
In a bowl, whisk the flour, cocoa powder, and ½ cup granulated sugar. Melt ¼ cup butter and stir it into the dry mix along with the eggs until smooth. Pour the batter into the pan and bake for 25 minutes, or until a toothpick comes out with a few moist crumbs.
While the cake bakes, make the caramel. In a small saucepan, combine the remaining ¼ cup granulated sugar with 2 tablespoons water. Cook over medium heat until the sugar turns amber. Carefully add the ½ cup heavy cream and ½ teaspoon smoked salt. Stir until smooth, then remove from heat.
Cool the cake in the pan for 10 minutes, then turn it out onto a plate. Drizzle the warm caramel over the cake.
In a chilled bowl, whip the remaining 1 cup heavy cream with the espresso powder, powdered sugar, and remaining ½ teaspoon smoked salt until soft peaks form. Spread the espresso whipped cream over the caramel layer just before serving.